Academic literature on the topic 'Area and perimeter of plane figures'

Some plane figures are interesting because their perimeter and area are numerically equal. For example, a square with a side of 4 cm has a perimeter and area numerically equal to sixteen. A further study of plane figures with this interesting property can be found in Bates (1979) and Markowitz (1981).

Random configurations are considered that are generated by a Poisson process of figures in the plane, and a recent result is used to derive formulae for the estimation of the number of figures, and their mean area and perimeter. The formulae require merely the determination of the area, the perimeter, and the Euler–Poincaré characteristic of the random configurations in a fixed field of view. There are no similar formulae for the standard deviations of the estimates; their magnitudes in typical cases are therefore assessed by Monte Carlo simulations.

Random configurations are considered that are generated by a Poisson process of figures in the plane, and a recent result is used to derive formulae for the estimation of the number of figures, and their mean area and perimeter. The formulae require merely the determination of the area, the perimeter, and the Euler–Poincaré characteristic of the random configurations in a fixed field of view. There are no similar formulae for the standard deviations of the estimates; their magnitudes in typical cases are therefore assessed by Monte Carlo simulations.

Objectives: The objectives of this study were to quantitatively estimate the number of mitotic figures (MFs) and evaluate the cellular and nuclear features of various histological grades of oral squamous cell carcinoma (OSCC) using Feulgen and 1% crystal violet stains. Methods: This case-control study took place at the Dr D. Y. Patil Dental College & Hospital in Mumbai, Maharashtra, India, between June and December 2016. A total of 51 samples were retrieved from the hospital archives. Of these, 15 well-differentiated, 15 moderately-differentiated and six poorly-differentiated OSCC samples formed the case group while 15 samples of normal gingival mucosa constituted the control group. Each sample was dyed using Feulgen and 1% crystal violet stains and the mitotic count, nuclear area (NA), cellular area (CA), nuclear perimeter (NP), cellular perimeter (CP) and nuclear-to-cytoplasmic (N/C) ratio was calculated using computeraided morphometry techniques. Results: The number of MFs visible per field was significantly higher in Feulgen-stained sections as compared to those stained with crystal violet (P = 0.050). In addition, the NA, NP, CA and CP values and N/C ratios of samples in the experimental group increased significantly in accordance with an increase in OSCC grade (P <0.001). Conclusion: The Feulgen stain is more reliable than 1% crystal violet in terms of the selective staining of MFs. Moreover, the findings of this study indicate that computer-based morphometric analysis is an effective tool for differentiating between various grades of OSCC.Keywords: Crystal Violet; Feulgen Stain; Mitotic Index; Image Cytometry; Squamous Cell Carcinoma; Oral Cancers.

ABSTRACTIn this work we report results of the research that references the title. The project was developed with fifth grade students; starting from the importance of mathematics in the training of primary school students, the great interest they have in ICT, the difficulties detected during the exercise of educational work. Important information was collected through a survey that was applied to the other teachers in charge of the orientation of the area of mathematics, which was reflected in the creation and application of a tool that allowed the student to assimilate assertively and motivating the learning of concepts Basic geometry in topics such as plane figures, angles, perimeters, area and volume.RESUMENEn este trabajo se reportan resultados de la investigación que referencia el título. El proyecto se desarrolló con estudiantes del grado quinto; partiendo de la importancia que tiene la matemática en la formación de los estudiantes de la básica primaria, del gran interés que ellos presentan hacia las TIC, las dificultades detectadas durante el ejercicio de la labor educativa. Se recolectó información importante mediante una encuesta que se aplicó a los demás docentes encargados de la orientación del área de matemáticas, lo que se vio reflejado en la creación y aplicación de una herramienta que permitió al estudiante asimilar de forma asertiva y motivadora el aprendizaje de conceptos básicos de la geometría en temas como las figuras planas, ángulos, perímetros, área y volumen.

Generally in high school, students learn how to find the length of straight lines and can use that information to find the perimeter and the length of the diagonal of simple polygons. They also learn the formula relating the diameter and the perimeter of a circle, and they know how to find the areas of circles, rectangles, triangles, and, possibly, regular n-gons. But the curves whose length and the figures whose area can be calculated by students are relatively mundane, and the methods are straightforward. The techniques used do not lend themselves easily to combining algebra and geometry

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This research treats the practice of the argumentation as teaching method, focusing the concepts of area perimeter of plane figures. Studies in national and international levels have already broached the subject, many times using the practice of the argumentation as method, not proposing, however, ways that demonstrate the functionality of that method. So this work answers the following question: in what measure the practice of the argumentation can present itself as method that contributes to the comprehension of concepts in mathematics taking as reference the case of the area and the perimeter of plane figures? To answer our question, we propose a didactic sequence modeled and analyzed with basis in the phases that compose the argumentative process, according to Toulmin (1996). The methodology of the study have been supported in Didactic Engineering purposes, the intervention have been effectuated with pupils at the fifth grade in Ensino Fundamental (students aged 10-11), using two argumentative institutions: the classroom and the informatics laboratory where we used the Geogebra software. The theoretical foundation have been based in speculative reflections by Toulmin (1996), in argumentative classification by Pedemonte (2002) and Cabassut (2005) and in the idea of argumentative convergence by Perelman and Olbrechts-Tyteca (2005). The analysis of the activities have evidenced that the practice of the argumentation contribute to the comprehension of the concepts of area and perimeter of plane figures, habilitating this practice as teaching method. The argumentative competences acquired by the pupils through the interactions with their classmates and the researchers about the subject allowed them have more autonomy to communicate and defend their ideas, respecting the opinion of the other classmates during the discussions, pay attention to the functionality and the possible validity of their argument, besides to learn specific symbols and language of mathematics
Esta pesquisa trata da prática da argumentação como método de ensino, focalizando os conceitos de área e perímetro de figuras planas. Estudos em níveis nacionais e internacionais já abordaram o assunto, muitas das vezes utilizando a prática da argumentação como método, sem, no entanto, propor caminhos que demonstrassem a funcionalidade dessa abordagem. Assim, este trabalho responde à seguinte questão: em que medida a prática da argumentação pode se apresentar como método que favoreça a compreensão de conceitos em matemática, tomando como referência o caso da área e perímetro de figuras planas? Como resposta, propomos uma sequência didática modelada e analisada com base nas fases que compõem o processo argumentativo segundo Toulmin (1996). A metodologia do estudo apoiou-se em pressupostos da Engenharia Didática e a intervenção foi efetivada com alunos do quinto ano do Ensino Fundamental (alunos de 10 a 11 anos), utilizando duas instituições argumentativas: a sala de aula e o laboratório de informática, no qual usamos o software Geogebra. A fundamentação teórica baseou-se nas reflexões teóricas de Toulmin (1996), na classificação de argumentos de Pedemonte (2002) e Cabassut (2005) e na idéia de convergência argumentativa de Perelman e Olbrechts-Tyteca (2005). As análises das atividades evidenciaram que a prática da argumentação favoreceu a compreensão dos conceitos de área e perímetro de figuras planas, habilitando essa prática como método de ensino. As competências argumentativas adquiridas pelos discentes, a partir das interações com colegas e pesquisador sobre o assunto em questão, possibilitaram- lhes ter mais autonomia para comunicar e defender suas ideias, respeitando a opinião do colega no decorrer das discussões, ficar atentos à funcionalidade e à validade ou não de seu argumento, além de apreender símbolos e linguagem específicos da matemática

This article takes up some details of Tamás Varga's legacy from the perspective of a former student. The focus is on his ideas, opinions, reviews and articles on mathematics education in secondary schools. Two school books had a special impact at that time in Hungary, the mathematics textbook (1949/50) by Rózsa Péter and Tibor Gallai for the 1st class of middle schools (14-15 years) and its continuation „Mathematics for the 1st class of middle schools“ (1956) by Tamás Varga and László Faragó. Some of the problems Tamás Varga posed in the Mathematical Journal (e.g. Farkas Bolyai's theorem about the decomposing equality of plane figures and problems with the object area of the definitions of plane figures) are also important. The following explanations refer to his articles on mathematics education and his dissertation on complex mathematics education (1975). Classification: A30, C10, D30, U20. Keywords: History of mathematics education, Hungarian math books for secondary schools, beginning of math lessons by guided discovery

Results of an experimental investigation on isolated synthetic jets in crossflow from rectangular orifices of different aspect ratio and orientation are presented. Three aspect ratios, AR = 4, 8, and 16, with pitch α = 90°, were investigated. Additionally, the AR = 8 case was pitched at 20°. The yaw angle, β, was varied through 0°, 10°, 45° and 90°. All orifices had same exit area and the data were compared with synthetic as well as steady jet from a circular orifice of same area. Hotwire measurements were performed to obtain all three components of mean velocity and turbulent stresses. Data were acquired for momentum-flux ratio up to J = 50. Distributions of time- and phase-averaged data were obtained on the cross sectional plane at x/D = 0.5, 5 and 10, as well as on the axial plane of the symmetry. Qualitative flowfield similarity between synthetic and steady jets is observed. However, high-momentum ‘cap’ above the low-momentum ‘dome’, characteristic of steady jets, does not necessarily appear in the synthetic jet. The position and shape of the high-momentum region depend on the distance from the orifice, pitch, yaw as well as momentum-flux ratio. Consequently, the location of the minimum velocity in the ‘dome’ measured at the plane of symmetry, ymin, is adopted as a reference for penetration estimate and trajectory comparison. For AR = 16, the dome is the largest in area with maximum velocity deficit. However, the penetration is somewhat higher for AR = 4. Increase in yaw reduces the spatial extent of the dome and the penetration height but augments the velocity deficit. At low J the dome is connected to the boundary layer and traces of the cap of high momentum fluid are visible above it. Increase in J lifts the dome and reorganizes the high-momentum fluid around its perimeter, eventually bringing it underneath. Phase-averaged data document dynamic topological changes within the cycle. Phase-averaged streamwise velocity contours on the cross-sectional plane exhibit behavior commensurate with that seen in time-averaged data at various J.

Keeping core parts of machines in proper condition is essential to improving productivity and quality of products. Metallic wear of knitting needles for circular knitting machines should be controlled within specific conditions. Currently, inspections of them are visually performed by skilled examiners, and automated inspection systems, which can measure 3-D shapes, are demanded. Because the needles have mirror glossed, complexly shaped surfaces, conventional lighting method, such as dome lights and diffuse on-axis lights, cannot irradiate the light evenly throughout the object and causes brightness unevenness, and that leads to 3-D measurement errors in image processors. To increase accuracy, we propose a new 3-D measurement system which equips omnidirectional EL (electroluminescence) lightings and DEHF (Dynamic Enhancement of High Frequency) method. Here, the system applies the shape from focus method, which moves the optical system vertically with respect to the fixed object and obtains a sequence of images that correspond to different levels of object focus. In the formation process of shallow depth of field microscopic images, a defocused imaging system plays the role of a low-pass filter. For this reason, the regions with high frequency components can be regarded as a focused area. The high frequency components are finally regarded as the contour of the object by the method. It recovers the 3-D shape of the object by estimation of height of the contours each image and arranging in the original order of the sequence of the height of the contours. The followings are novelties of our proposed system. Firstly, omnidirectional EL lightings irradiate an object with uniform lights from all directions. They are composed of the following lights: coaxial through objective lens, object lens perimeter, side and bottom lights, and each of which can adjust brightness; therefore they can reduce unevenness of brightness on the object. We adopted inorganic EL sheet as the lighting device. EL sheet is capable of plane emission and prevent the occurrence of the unevenness of the irradiated light by the point source of light. Secondly, algorithm for shape from focus can be improved by our DEHF method. Even if the above lightings are applied, there still remains low frequency non-uniformity of brightness. DEFH method removes the low frequency by subtracting mean filtered image from original one, and remaining high frequency content can be emphasized. We built a microscope based prototype system and conducted experiments. Through them, the validity of our proposed method was confirmed.

This report provides two sets of equations for estimating peak discharge quantiles at annual exceedance probabilities (AEPs) of 0.50, 0.20, 0.10, 0.04, 0.02, 0.01, 0.005, and 0.002 (recurrence intervals of 2, 5, 10, 25, 50, 100, 200, and 500 years, respectively) for watersheds in Illinois based on annual maximum peak discharge data from 117 watersheds in and near northeastern Illinois. One set of equations was developed through a temporal analysis with a two-step least squares-quantile regression technique that measures the average effect of changes in the urbanization of the watersheds used in the study. The resulting equations can be used to adjust rural peak discharge quantiles for the effect of urbanization, and in this study the equations also were used to adjust the annual maximum peak discharges from the study watersheds to 2010 urbanization conditions. The other set of equations was developed by a spatial analysis. This analysis used generalized least-squares regression to fit the peak discharge quantiles computed from the urbanization-adjusted annual maximum peak discharges from the study watersheds to drainage-basin characteristics. The peak discharge quantiles were computed by using the Expected Moments Algorithm following the removal of potentially influential low floods defined by a multiple Grubbs-Beck test. To improve the quantile estimates, regional skew coefficients were obtained from a newly developed regional skew model in which the skew increases with the urbanized land use fraction. The skew coefficient values for each streamgage were then computed as the variance-weighted average of at-site and regional skew coefficients. The drainage-basin characteristics used as explanatory variables in the spatial analysis include drainage area, the fraction of developed land, the fraction of land with poorly drained soils or likely water, and the basin slope estimated as the ratio of the basin relief to basin perimeter. This report also provides: (1) examples to illustrate the use of the spatial and urbanization-adjustment equations for estimating peak discharge quantiles at ungaged sites and to improve flood-quantile estimates at and near a gaged site; (2) the urbanization-adjusted annual maximum peak discharges and peak discharge quantile estimates at streamgages from 181 watersheds including the 117 study watersheds and 64 additional watersheds in the study region that were originally considered for use in the study but later deemed to be redundant. The urbanization-adjustment equations, spatial regression equations, and peak discharge quantile estimates developed in this study will be made available in the web-based application StreamStats, which provides automated regression-equation solutions for user-selected stream locations. Figures and tables comparing the observed and urbanization-adjusted peak discharge records by streamgage are provided at http://dx.doi.org/10.3133/sir20165050 for download.

The article investigates functional techniques of extralinguistic expression in multimedia texts; the effectiveness of figurative expressions as a reaction to modern events in Ukraine and their influence on the formation of public opinion is shown. Publications of journalists, broadcasts of media resonators, experts, public figures, politicians, readers are analyzed. The language of the media plays a key role in shaping the worldview of the young political elite in the first place. The essence of each statement is a focused thought that reacts to events in the world or in one’s own country. The most popular platform for mass information and social interaction is, first of all, network journalism, which is characterized by mobility and unlimited time and space. Authors have complete freedom to express their views in direct language, including their own word formation. Phonetic, lexical, phraseological and stylistic means of speech create expression of the text. A figurative word, a good aphorism or proverb, a paraphrased expression, etc. enhance the effectiveness of a multimedia text. This is especially important for headlines that simultaneously inform and influence the views of millions of readers. Given the wide range of issues raised by the Internet as a medium, research in this area is interdisciplinary. The science of information, combining language and social communication, is at the forefront of global interactions. The Internet is an effective source of knowledge and a forum for free thought. Nonlinear texts (hypertexts) – «branching texts or texts that perform actions on request», multimedia texts change the principles of information collection, storage and dissemination, involving billions of readers in the discussion of global issues. Mastering the word is not an easy task if the author of the publication is not well-read, is not deep in the topic, does not know the psychology of the audience for which he writes. Therefore, the study of media broadcasting is an important component of the professional training of future journalists. The functions of the language of the media require the authors to make the right statements and convincing arguments in the text. Journalism education is not only knowledge of imperative and dispositive norms, but also apodictic ones. In practice, this means that there are rules in media creativity that are based on logical necessity. Apodicticity is the first sign of impressive language on the platform of print or electronic media. Social expression is a combination of creative abilities and linguistic competencies that a journalist realizes in his activity. Creative self-expression is realized in a set of many important factors in the media: the choice of topic, convincing arguments, logical presentation of ideas and deep philological education. Linguistic art, in contrast to painting, music, sculpture, accumulates all visual, auditory, tactile and empathic sensations in a universal sign – the word. The choice of the word for the reproduction of sensory and semantic meanings, its competent use in the appropriate context distinguishes the journalist-intellectual from other participants in forums, round tables, analytical or entertainment programs. Expressive speech in the media is a product of the intellect (ability to think) of all those who write on socio-political or economic topics. In the same plane with him – intelligence (awareness, prudence), the first sign of which (according to Ivan Ogienko) is a good knowledge of the language. Intellectual language is an important means of organizing a journalistic text. It, on the one hand, logically conveys the author’s thoughts, and on the other – encourages the reader to reflect and comprehend what is read. The richness of language is accumulated through continuous self-education and interesting communication. Studies of social expression as an important factor influencing the formation of public consciousness should open up new facets of rational and emotional media broadcasting; to trace physical and psychological reactions to communicative mimicry in the media. Speech mimicry as one of the methods of disguise is increasingly becoming a dangerous factor in manipulating the media. Mimicry is an unprincipled adaptation to the surrounding social conditions; one of the most famous examples of an animal characterized by mimicry (change of protective color and shape) is a chameleon. In a figurative sense, chameleons are called adaptive journalists. Observations show that mimicry in politics is to some extent a kind of game that, like every game, is always conditional and artificial.